Fair Division and Collective Welfare

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MIT Press, Aug 20, 2004 - Business & Economics - 289 pages

The concept of fair division is as old as civil society itself. Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice. Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare.

The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness. It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses. The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method.

The Shapley value is the single most important contribution of game theory to distributive justice. A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality. The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence. The book contains a wealth of empirical examples and exercises.

 

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Contents

Microeconomic Foundations
1
Cardinal
3
Ordinal
6
14 Externalities and Fair Division
9
15 Private versus Public Contracts
13
16 Organization and Overview of the Book
15
17 Introduction to the Literature
18
Fair Distribution
21
Exercises to Chapter 4
131
The Shapley Value
139
Definition
143
53 The Standalone Test and Standalone Core
147
54 Standalone Surplus
156
55 Axiomatizations of the Shapley Value
159
56 Introduction to the Literature
162
Exercises to Chapter 5
163

22 A Simple Model of Fair Distribution
27
23 Contested Garment Method
37
24 Equal Sacrifice in Taxation
41
25 SumFitness and Equality
44
26 Introduction to the Literature
51
Exercises to Chapter 2
52
Cardinal Welfarism
63
32 Additive Collective Utility Functions
66
33 Egalitarianism and the Leximin Social Welfare Ordering
70
34 Comparing Classical Utilitarianism Nash and Leximin
76
35 Failures of Monotonicity
81
36 Bargaining Compromise
86
37 Introduction to the Literature
95
Exercises to Chapter 3
96
Voting and Social Choice
107
42 Condorcet versus Borda
110
43 Voting over Resource Allocation
116
44 SinglePeaked Preferences
118
45 Intermediate Preferences
122
46 Preference Aggregation and Arrows Theorem
126
47 Introduction to the Literature
130
Managing the Commons
169
62 Constant Returns to Scale
173
Three Interpretations
175
Decreasing Returns
184
65 Increasing Returns
190
66 Axiomatic Comparison of the Three Solutions
199
67 Introduction to the Literature
208
Exercises to Chapter 6
209
Fair Trade and Fair Division
221
72 Imperfect Competition
228
73 Destructive Competition
232
74 No Envy and the Assignment Problem
235
75 The CEEI and Egalitarian Equivalent Solutions
240
76 Axiomatics of Fair Division
248
77 Introduction to the Literature
251
Exercises to Chapter 7
252
A Glossary of Definitions and Results
261
References
277
Index
281
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About the author (2004)

Herv Moulin is George A. Peterkin Professor of Economics at Rice University.

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